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Speedy Sidney

Age 11 to 14 Challenge Level:

Two trains set off at the same time from each end of a single straight railway line which is 100 km long.

The first train travels at a constant speed of 55 km/h. The second train travels at a constant speed of 70 km/h.

A very fast bee, Sidney travels at 100 km/h. Sidney starts off in front of the first train and flies continuously back and forth between the two trains.

How far does Sidney fly before he is squashed between the two trains?

How could you alter the problem so that Sidney flies exactly 100 km?

(Apologies to bee lovers everywhere!)